Math word problem (MWP) solving is an important task in question answering which requires human-like reasoning ability. Analogical reasoning has long been used in mathematical education, as it enables students to apply common relational structures of mathematical situations to solve new problems. In this paper, we propose to build a novel MWP solver by leveraging analogical MWPs, which advance the solver’s generalization ability across different kinds of MWPs. The key idea, named analogy identification, is to associate the analogical MWP pairs in a latent space, i.e., encoding an MWP close to another analogical MWP, while leaving away from the non-analogical ones. Moreover, a solution discriminator is integrated into the MWP solver to enhance the association between an MWP and its true solution. The evaluation results verify that our proposed analogical learning strategy promotes the performance of MWP-BERT on Math23k over the state-of-the-art model Generate2Rank, with 5 times fewer parameters in the encoder. We also find that our model has a stronger generalization ability in solving difficult MWPs due to the analogical learning from easy MWPs.
Math word problem (MWP) solving faces a dilemma in number representation learning. In order to avoid the number representation issue and reduce the search space of feasible solutions, existing works striving for MWP solving usually replace real numbers with symbolic placeholders to focus on logic reasoning. However, different from common symbolic reasoning tasks like program synthesis and knowledge graph reasoning, MWP solving has extra requirements in numerical reasoning. In other words, instead of the number value itself, it is the reusable numerical property that matters more in numerical reasoning. Therefore, we argue that injecting numerical properties into symbolic placeholders with contextualized representation learning schema can provide a way out of the dilemma in the number representation issue here. In this work, we introduce this idea to the popular pre-training language model (PLM) techniques and build MWP-BERT, an effective contextual number representation PLM. We demonstrate the effectiveness of our MWP-BERT on MWP solving and several MWP-specific understanding tasks on both English and Chinese benchmarks.
This paper studies solving Arabic Math Word Problems by deep learning. A Math Word Problem (MWP) is a text description of a mathematical problem that can be solved by deriving a math equation to reach the answer. Effective models have been developed for solving MWPs in English and Chinese. However, Arabic MWPs are rarely studied. This paper contributes the first large-scale dataset for Arabic MWPs, which contains 6,000 samples of primary-school math problems, written in Modern Standard Arabic (MSA). Arabic MWP solvers are then built with deep learning models and evaluated on this dataset. In addition, a transfer learning model is built to let the high-resource Chinese MWP solver promote the performance of the low-resource Arabic MWP solver. This work is the first to use deep learning methods to solve Arabic MWP and the first to use transfer learning to solve MWP across different languages. The transfer learning enhanced solver has an accuracy of 74.15%, which is 3% higher than the solver without using transfer learning. We make the dataset and solvers available in public for encouraging more research of Arabic MWPs: https://github.com/reem-codes/ArMATH
Many existing works have demonstrated that language is a helpful guider for image understanding by neural networks. We focus on a language-shaped learning problem in a few-shot setting, i.e., using language to improve few-shot image classification when language descriptions are only available during training. We propose a data-efficient method that can make the best usage of the few-shot images and the language available only in training. Experimental results on dataset ShapeWorld and Birds show that our method outperforms other state-of-the-art baselines in language-shaped few-shot learning area, especially when training data is more severely limited. Therefore, we call our approach data-efficient language-shaped learning (DF-LSL).